Related question: this topic is examined
Linear Independence
Linear independence and dependence of vectors and of a matrix’s columns, special cases (one vector, two vectors, more vectors than entries, the zero vector).
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Linear independence
Exam angle
Related question: this topic is examined
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Linearly Linearly independent A Set of One dependent
FACT
Notes
Facts: a set containing 0 is dependent; two vectors are dependent ⇔ one is a multiple of the other; MORE vectors than entries (p > n) ⇒ dependent.
Memory trick p vectors in ℝⁿ with p > n are always dependent.
Exam angle
Four vectors in ℝ³ are:
If a set contains the zero vector, it is linearly dependent.
Example:
Example:
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